广义量词理论对一阶逻辑的扩展

广义量词理论是一阶逻辑的扩展。该理论已经成为逻辑学和语言学中重要的推理工具之一。广义量词是对来自于一阶逻辑中两个标准量词（全称量词和存在量词）的推广。对一阶逻辑进行扩展的主要原因有二：其一是为了解释亚氏三段论形式以外的大量的有效推理；其二是为了提升一阶逻辑的表达力，使得计算机能够更好地处理自然语言。文章阐述了广义量词理论来自于哪里，是如何得来的。现代谓词逻辑首先通过固定一阶逻辑中的全称量词和存在量词的真值定义，然后把它们的真值定义推广到〈1〉类型的广义量词，之后把〈1〉类型的广义量词的真值定义推广到任意的广义量词。这样就可以把任意的广义量词添加到一阶逻辑中，从而得到表达力更强的逻辑———广义量词理论。

Extension of First-Order Logic by Generalized Quantifier Theory

Generalized quantifier theory is the extension of first-order logic.The theory is now one of important tools of reasoning equipment in logic and linguistics.The term “generalized quantifier”re-flects that these entities were introduced in logic as generalizations of the standard quantifiers from first-order logic,universal and existential quantifier.The main reasons for the extension of first-order logic are two:the one is to explain many of valid syllogistic forms beyond Aristotlian syllogisms;the other is to enhance the expressive power of first-order logic,so that the computer can better deal with natural language.The main purpose of this paper is to describe where and how generalized quantifier theory comes from.Modern predicate logic firstly fixed the meaning of universal and existential quanti-fier with the respective clauses in the truth definition,then generalized the definition of them to the one of generalized quantifiers of type 〈1 〉,and then generalized the latter to the one of generalized quantifiers of arbitrary types.Hence one can add any generalized quantifier first-order logic in order to gain more expressive logic:generalized quantifier theory.